Atlas Trail
The Millennium Prize Problems: Seven Problems, One Solved
In 2000 the Clay Mathematics Institute named seven problems it considered the deepest open questions in mathematics, and put a million dollars on each one. Only one has fallen since: Grigori Perelman's proof of the Poincare Conjecture, a prize he refused to collect. This trail visits all seven, the one that is settled and the six that still are not.
Stop 1 of 7.
Theorems
The one Millennium Prize Problem that is solved: Henri Poincare's 1904 question about three dimensional spheres, closed by Grigori Perelman in 2003, and the prize he declined to accept.
Stop 2 of 7.
Conjectures
Widely called the most important unsolved problem in pure mathematics: where do the zeros of the Riemann zeta function really lie?
Stop 3 of 7.
Conjectures
Is every problem whose solution is easy to check also easy to solve? A question that shapes what computers can and cannot do quickly.
Stop 4 of 7.
Conjectures
Found experimentally on an early Cambridge computer in the 1960s: a bridge between an elliptic curve's rational points and its L-function.
Stop 5 of 7.
Conjectures
Posed in 1950: does the topology of a complex algebraic variety always come from actual algebraic subvarieties?
Stop 6 of 7.
Conjectures
The equations that describe how water and air actually flow, written in the nineteenth century; whether their solutions always behave, nobody yet knows.
Stop 7 of 7.
Conjectures
Physics has measured the mass gap in experiment and simulation for decades; mathematics still cannot derive it from first principles.
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